
where \(m^2\equiv 2(b_2-6\gamma ^2)\) . The first term is the negative cosmological constant (we fix the AdS radius to one). According to the AdS/CFT dictionary, the scalar field \(\phi \)  in the bulk is dual to a scalar operator in the dual boundary field theory \(O_\phi \)  which is known as field-operator correspondence [1]}, [2]}. The conformal dimension of the scalar operator, \(\Delta \) , is related to the mass of the scalar field in the bulk through \(\Delta (\Delta -4)=m^2\) . Holographically, the presence of the dilaton field in the bulk is dual to a deformation of the boundary conformal field theory
\(\mathcal {L}= \mathcal {L}_{\text{CFT}}+\Lambda ^{4-\Delta }O_{\phi },\) 
